SIAM Journal on Scientific Computing
Volume 24, Number 6
pp. 1919-1929

Numerical Computations of Viscous, Incompressible Flow Problems Using a Two-Level Finite Element Method

Faisal Fairag

Abstract. We consider two-level finite element discretization methods for the stream function formulation of the Navier--Stokes equations. The two-level method consists of solving a small nonlinear system on the coarse mesh and then solving a linear system on the fine mesh. The basic result states that the errors between the coarse and fine meshes are related superlinearly. This paper demonstrates that the two-level method can be implemented to approximate efficiently solutions to the Navier--Stokes equations. Two fluid flow calculations are considered to test problems which have a known solution and the driven cavity problem. Stream function contours are displayed showing the main features of the flow.

Key words. two-level method, Navier--Stokes equations, finite element, stream function formulation, Reynolds number

AMS Subject Classifications. 65N35, 76M30, 76D05

DOI. 10.1137/S1064827500370895